Ruler device for decimal-octal conversion

ABSTRACT

A flat disc having a series of scales imprinted thereon including a main scale on a 360* circle divided into 100 parts, an inner scale which is one-eighth of the main scale, a first outer scale which is a periodic 7 scale and a second outer scale of another color which is the periodic 7 scale shifted in phase by 4. A radially disposed indicator arm pivots around the central axis on the surface of the flat disc to coordinate the scales thereon and make the decimal-octal conversion.

United States Patent [191 [111 3,843,048 Haase Oct. 22, 1974 4] RULER DEVICE 'FOR DEClMAL-OCTAL CONVERSION Inventor: Kurt H. Haase, 148 Standish Rd.,

Watertown, Mass. 02172 Filed: Nov. 5, 1973 Appl. No.: 412,857

vs. C! 235/84, 235/70 A, 235/88 rm. Cl G06g 1/02 Field of Search 235/88, s3, s4, 78, 70 R,

References .Cited UNITED STATES PATENTS 4/1972 Wyatt et al. 235/84 ZlO e543 7654 e o z Primary Examiner-Stephen .l. Tomsky Attorney, Agent, or Firm-Harry A. Herbert, Jr.; Arsen Tashjian [5 7] ABSTRACT main scale, a first outer scale which is a periodic 7 scale and a second outer scale of another color which is the periodic 7 scale shifted in phase by 4. A radially disposed indicator arm pivots around the central axis on the surface of the fiat disc to coordinate the scales thereon and make the decimal-Octal conversion.

3 Claims, 2 Drawing Figures .1 I RULERDEVICE FOR DECIMAL-OCTAL CONVERSION BACKGROUND OF THE INVENTION This invention relates to a device for decimal to octal conversion of integers and vice versa and, more particularly, the invention is concerned with providing a relatively simple and accurate means for converting a decimal number to its octal equivalent by the use of a ruler device wherein the conversion is obtained directly therefrom.

In working with computers it is very often necessary to convert decimal numbers into their octal equivalents. The procedure presently in use to accomplish this conversion is described in several printed publications, for instance, McGraw-Hill Encyclopedia of Science and Technology, Vol. 9, pages 223. As can be seen from this publication and the following example, the conversion process becomes very tedious for high digit numbers and, consequently, subject to errors and miscalculations.

To find the octal equivalent of the decimal number 88,012 in the manner presently in use, the number denoted as 88,012 is essentially divided by 8. However,

unlike the regular division system where one is interested in the integer quotient and the final remainder, in the decimal to octal conversion one is primarily interested in the series of remainders obtained in the necessary steps of the division procedure. These remainders arranged successively from right ,to left represent the octal equivalent in juxtaposition. In each division step the remainder is in the range of the integers from O to 7. The remainder in the first division step is the least significant digit of the octal number, the one in the second step is the next digit in the octal number in the direction to the left, and so forth until the division process is completed.

It would be most desirable to provide a device wherein the conversion of the decimal to octal conversion or vice versa could be easily accomplished without the requirement of tedious division steps wherein errors in calculation might be expected to occur.

SUMMARY OF THE INVENTION The present invention is concerned with providing a device to ease the process of decimal to octal conversion and vice versa. The device includes a flat disc or ground plate upon which are imprinted a series of related scales arranged in circles around its center and a radially disposed indicator arm pivotable around the center of the disc. The main scale is a 360 circle divided into 100 parts and a concentric inner scale includes figures which are related by a factor of 8 with the main scale. Outside the main scale is a periodic 7 scale and outside this scale is another periodic 7 scale that is shifted in phase by 4.

Accordingly, it is an object of the invention to provide a means for converting a number expressed in the decimal system to its corresponding octal system equivalent and vice versa.

Another object of the invention is to provide a device which will eliminate the need for tedious arithmetical calculations normally required for decimal to octal conversion in computer work.

Still another object of the invention is to provide an efficient decimal-octal conversion device which is simple to use by relatively untrained personnel and which requires only a minimum of simple movements to accurately make the necessary conversion.

A further object of the invention is to provide a device which is simple and easy to construct in quantity for general use in computer work and which reduces the chance of error while at the same time permits more rapid and accurate determination of the necessary information. v

These and other objects, features, and advantages will become more apparent after considering the following detailed description taken in conjunction with the annexed drawings and appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a top plan view of the ruler device according to the invention showing the relative positions of the various scales and the radially disposed pivotably mounted indicator arm; and

FIG. 2 is a sectional view taken along the line 22 of FIG. 1.

DESCRIPTION OF.A PREFERRED EMBODIMENT Referring now to the drawings, there is shown a preferred embodiment of the ruler device for decimaloctal conversion according to the invention. The device includes a flat disc 13 constructed of cardboard, plastic, metal or the like having a series of circular scales imprinted thereon around the central axis 15. A pivotably mounted radially disposed arm 17 is positioned on the disc 13 and arranged to rotate around the axis 15. A radial index line 19 is marked along the center of the arm 17.

In the embodiment herein described, there are four concentric scales imprinted on the surface of the disc 13. One scale identified by the reference numeral 21 can be referred to as the main scale and serves to divide the 360 circle into equal parts. A second scale positioned concentrically inside the main scale 21 and referred to as the inner scale 23 operates in effect to divide the main scale 21 by eight. Thus, the inner scale 23 and the main-scale 21 represent a factor 8 table. Immediately outside the main scale 21 there is concentrically positioned an arrangement of numbers 1 to 7 periodically repeated which can be referred to as the first outer scale 25. This first outer scale 25 is preferably marked in the color black and in certain instances indicates the remainder number during the conversion process. Outside the first outer scale 25 there is concentrically positioned a second outer scale 27 which is also an arrangement of numbers l-7 periodically repeated but is shifted in phase by four. This second outer scale 27 is preferably marked in the color red to distinguish from the first outer scale 25 and is useful to indicate the remainder number in certain of the other conversion steps.

MODE OF OPERATION The operation of the hereinbefore device is based upon the principle that certain high digit decimal numbers are divisible by 8 and certain ones are not and this can be quickly recognized by considering the three least significant digits only as follows. If the third one from the right end is even the number is divisible by 8 if the number consisting of the two least significant digits is divisible by 8. If the number is less than three digits in size, the third digit from right is zero and consequently even. if the third digit from right in the original number is odd, the number is divisible by 8 if the last two digits at the right end are divisible by 4, but not by 8. Thus 856 is divisible by 8, but 756 is not. But 744. is divisible by 8. It does not matter how far these numbers extend to the left.

Based on this principle, the hereinbefore described device presents the remainder for a number of anydigit size when divided by 8. All that has to be done to find this remainder is to set the line 19 of the arm 17 on the number on the main scale 21 that is theleast significant two digit part of the number to be converted. 1f the third digitfrom the right in this number is even, the remainder is found on thefirst outer (black) scale 25, andif the number is; odd, the remainder is found on the second outer (red) scale 27.

- For example: to convert the decimal number 88,0l2 -to its octal equivalent:

First step: set the line 19 on 12 (the two least significant digits in 88,012) on the main scale 21, find first remainder 4 whichis the least significant digit of octal number on the black remainder scale 25 since the third from right digit in 88,012 is even. Subtract 4 from 88,012 to obtain 88,008, then divide by 8 which equals 1 1,001.' I

Second step: set the line'19 on 1 on the main scale 2l, find remainder l which is the second digit from right in the octal number on the black remainder scale 25 since the third digit in 11,001 is even. Subtract 1 from 11,001 to obtain 11,000, then divide by 8 which equals 1,375.

Third step: set the line 19 on 75 on the main scale 21, find remainder 7 which is thelthird digit from right in the octal number on the red remainder. scale 27 since 0, then the procedure is at its end. The result is 88,012 equals 2515,714 I Note that besides finding the remainders as described above, the ruler device is useful for dividing the numbers reduced by the remainder to avoid miscalculations. This is accomplished by using the inner scale 23 to-obtain the quotient of the figure on the main'scale 21. The multiplication process can be carried out in a similar manner by using the same scales in reverse.

Although the invention has been illustrated and described in'terms of a preferred embodiment thereof, it will be apparent to those skilled in the art that certain changes alterations, modifications and substitutions, particularly with respect to the construction details, can be made in the arrangement and location'of the various scales without departing from the true spirit and scope of the appended claims. Also, it should be noted that the element 17 which is described as a pivotably mounted radially disposed arm could be replaced by a clear plastic disc rotatably mounted with a radial index line marked thereon.

Having thus set forth and disclosed the natureof my invention, whatl claim is:

thethirddigit in 1,375 is odd. Subtracll from 1,375

' to obtain 1,368, then divide by 8 which equals 171.

Fourth step: set the line 19 on 71 on the main scale 21, find the remainder 3 which is the fourth digit from the right in the octal number on the red remainder scale 27 since the third digit in 171 is odd. Subtract 3 Sixth step: Set the line 19 on 2 on the main scale 21, find the remainder 2 which is. the sixth digit from the right in the octal number. Subtract 2 from 2 to obtain 1. A ruler device for decimal-octal conversion of numbers used in computer work comprising a flat disc having a central axis with a series of scales imprinted therearound, one of said scales being the main scale comprising a 360 circle divided into 100 parts, a first outer scale positioned outside said main scale and concentrically therewith, said first outer scale being marked in periodic repetition of 7 to represent the remainder in some selected cases, a second outer scale positioned outside said first outer scale and concentrically therewith, said second outer scale being marked in periodic repetition of 7 shifted in phase by 4 from said first outer scale to represent the remainder in other selected cases, and a pivotable radially disposed indicator arm mounted on said flat disc for rotation around the central axis thereof, said indicator arm having a radial index line passing through all of the scales imprinted on said disc such that reference to the proper outer scale will indicate theoctal number corresponding to the decimal number on the main scale under the index line.

2. The ruler device defined in claim 1 wherein an inner scale is positioned withinsaid main scale and concentric therewith, said inner scale being marked to represent a factor 8 table with said main scale.

3. The ruler device defined in claim 1 wherein the first and second outer scales are imprinted in different colors to facilitate the finding of the proper octal number. 

1. A ruler device for decimal-octal conversion of numbers used in computer work comprising a flat disc having a central axis with a series of scales imprinted therearound, one of said scales being the main scale comprising a 360* circle divided into 100 parts, a first outer scale positioned outside said main scale and concentrically therewith, said first outer scale being marked in periodic repetition of 7 to represent the remainder in some selected cases, a second outer scale positioned outside said first outer scale and concentrically therewith, said second outer scale being marked in periodic repetition of 7 shifted in phase by 4 from said first outer scale to represent the remainder in other selected cases, and a pivotable radially disposed indicator arm mounted on said flat disc for rotation around the central axis thereof, said indicator arm having a radial index line passing through all of the scales imprinted on said disc such that reference to the proper outer scale will indicate the octal number corresponding to the decimal number on the main scale under the index line.
 2. The ruler device defined in claim 1 wherein an inner scale is positioned within said main scale and concentric therewith, said inner scale being marked to represent a factor 8 table with said main scale.
 3. The ruler device defined in claim 1 wherein the first and second outer scales are imprinted in different colors to facilitate the finding of the proper octal number. 